Your parent’s mortgage is $231,450 at a 4.65% APR. If they pay $2,236 toward the mortgage each month, how much of the second month's payment is applied toward the second month's principal?

Question

(1 point)
Responses

$2,678.26
$2,678.26

$4,437.34
$4,437.34

$1,339.13
$1,339.13

$1,344.32

Answer 1

To determine how much of the second month's payment goes toward the principal of the mortgage, we need to calculate the interest for the second month and then subtract that from the total monthly payment.

1. Calculate the monthly interest rate:

   • APR = 4.65%
   • Monthly interest rate = 4.65% ÷ 12 = 0.3875% = 0.003875 (as a decimal)

2. Calculate the interest for the first month:

   • Initial mortgage amount (principal) = $231,450
   • Interest for the first month = Principal × Monthly interest rate
   • Interest for the first month = $231,450 × 0.003875 ≈ $896.78

3. Calculate the principal paid in the first month:

   • Monthly payment = $2,236
   • Principal payment for the first month = Monthly payment - Interest for the first month
   • Principal payment for the first month = $2,236 - $896.78 ≈ $1,339.22

4. Calculate the remaining principal after the first month:

   • Remaining principal after first payment = Initial principal - Principal paid in first month
   • Remaining principal = $231,450 - $1,339.22 ≈ $230,110.78

5. Calculate the interest for the second month:

   • Interest for the second month = Remaining principal × Monthly interest rate
   • Interest for the second month = $230,110.78 × 0.003875 ≈ $891.10

6. Calculate the principal paid in the second month:

   • Principal payment for the second month = Monthly payment - Interest for the second month
   • Principal payment for the second month = $2,236 - $891.10 ≈ $1,344.90

Thus, about $1,344.90 of the second month’s payment is applied toward the principal of the mortgage. The closest answer choice in the provided responses is $1,344.32.